Free vibration analysis of rotating piezoelectric bar of circular cross section immersed in fluid

Free vibration analysis of rotating piezoelectric bar of circular cross-section immersed in fluid is discussed using three-dimensional theory of piezoelectricity. The equations of motion of the bar are formulated using the constitutive equations of a piezoelectric material. The equations of motion of the fluid are formulated using the constitutive equations of an inviscid fluid. Three displacement potential functions are introduced to uncouple the equations of motion, electric conduction. The perfect-slip boundary conditions are applied at the solid-fluid interfaces to obtain the frequency equation of the coupled systems. The frequency equations are obtained for longitudinal and flexural (symmetric and antisymmetric) modes of vibration and are studied numerically for PZT-4 material. The computed wave number and electro mechanical coupling is presented in the form of dispersion curves. The secant method is used to obtain the roots of the frequency equation.